JEE MATHEMATICS MCQ: MATHEMATICAL INDUCTION

1 Easy

1 of 1

Analyzing +4 | -1

Statement I:- P(n) is a true statement

\forall n \geqslant 1;\& n \notin N

P(n)

is true for

n = t\& t + 1

where

t \in N

equal to set of natural numbers
Statement II:- Any statement

P(n)

is true

\forall n \in N

by the principle of finite mathematical
induction. Where

N =

set of natural numbers

View answer and explanation

Correct option: C

I is true, II is true and is a correct explanation for I

I is false, II is true. The principle of mathematical induction applies only to natural numbers, not to all real numbers greater than or equal to 1.

More Questions from MATHEMATICAL INDUCTION

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\frac{1^2}{3}+\frac{1^2+2^2}{5}+\frac{1^2+2^2+3^2}{7}+\ldots

n

P\left( n \right):2 + 4 + 6 \ldots + \left( {2n} \right),\;n \in N,

\begin{array}{l} P\left( k \right) = k\left( {k + 1} \right) + 2\mathrm{implies}\\ P\left( k \right) = \left( {k + 1} \right)\left( {k + 2} \right) + 2 \end{array}

k \in N.

P\left( n \right) = n\left( {n + 1} \right) + 2

n

n

a\left( n \right) = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ... + \frac{1}{{\left( {{2^n}} \right) - 1}}.

n(n+1)(n+2)(n+3)

n \in N

12 {~N}

8 {~m}

6 {~m}